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A Survey of Bicooperative Games

In: Pareto Optimality, Game Theory And Equilibria

Author

Listed:
  • Jesús M. Bilbao

    (University of Seville)

  • Julio R. Fernández

    (University of Seville)

  • Nieves Jiménez

    (University of Seville)

  • Jorge J. López

    (University of Seville)

Abstract

The aim of the current chapter is to study several solution concepts for bicooperative games. For these games introduced by Bilbao [1], we define a one-point solution called the Shapley value, as this value can be interpreted in a similar way to the classic Shapley value for cooperative games. The first result is an axiomatic characterization of this value. Next, we define the core and the Weber set of a bicooperative game and prove that the core of a bicooperative game is always contained in the Weber set. Finally, we introduce a special class of bicooperative games, the so-called bisupermodular games, and show that these games are the only ones in which the core and the Weber set coincide.

Suggested Citation

  • Jesús M. Bilbao & Julio R. Fernández & Nieves Jiménez & Jorge J. López, 2008. "A Survey of Bicooperative Games," Springer Optimization and Its Applications, in: Altannar Chinchuluun & Panos M. Pardalos & Athanasios Migdalas & Leonidas Pitsoulis (ed.), Pareto Optimality, Game Theory And Equilibria, pages 187-216, Springer.
    • Handle: RePEc:spr:spochp:978-0-387-77247-9_8
    DOI: 10.1007/978-0-387-77247-9_8
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